The period map and the intersection form

Abstract

Let us be given a smooth fibration and a differential form on the space of fibration which is closed on the fibres. In such a situation there arises the period map of the form – a many-valued map from the base of the fibration to the cohomology of the fibre. A point of the base is mapped to the cohomology class of the form in the fibre over the point translated to the cohomology of a distinguished fibre. The fact that it is many-valued arises from the fact that there is not a unique choice of path for the translation.